Get in contact with a realtor and tell them what your looking for cause to be frank some of these people are completely out to lunch. If your in your mid 20's don't be taking advice from some 60 year old guy who's scared of downtown and thinks panhandlers woudl knife them.

I'm not much older than you. If I was single and looking to buy a place and working downtown, my top choices would be:
1. Exchange district
2. Osborne / Corydon Village
3. St. Boniface

and if you want to rent, downtown or the village is where i would look. A few high rises in the vilalge and tonnes of choices downtown.

the avenue building was just completed a conversion to apartments. Located just down the street from MTS Centre. Its looking sweet:

I seriously go downtown all the time for clubs , bars, restaurants. My grilfriend rents an apartment downtown. Not once have I ever felt threatened. If you're not looking for trouble you won't find it.